1. Field of the Invention
The present invention relates to a liquid crystal tuned birefringent filter and, more particularly, to an electrically tunable filter including stacked birefringent liquid crystal cells.
2. Description of the Prior Art
The principle of the birefringent filter was first suggested by the French astronomer Bernard Lyot in 1933. Lyot constructed filters having a half-bandwidth of about five angstroms and used them for photographing the solar corona in monochromatic light. The Lyot-type filter consists of a stack of elements, each of which consists of a birefringent cell, i.e. a retarder, and a polarizer. For a further discussion of a Lyot-type filter, reference should be made to U.S. Pat. No. 2,718,170, issued Sept. 20, 1955 to Bernard Lyot and entitled Slitless Spectrophotometer.
Birefringent cells have the property that their refractive index, hence the velocity of propagation of light therethrough, varies with direction through the element. Such materials are said to be anisotropic. When a polarized light beam passes through a birefringent cell, the beam breaks into two orthogonally polarized components called the ordinary and extraordinary rays, which propagate with velocities which are inversely proportional to the two refractive indices existing in the directions of beam propagation. These two beams emerge from the birefringent cell with a difference in phase angles. The resultant beam, in general, is said to be elliptically polarized.
When the elliptically-polarized light beam passes through a polarizer, only those components of the beam with their electric vectors in the plane of polarization of the polarizer pass therethrough. The two component beams then interfere and the intensity of the resultant beam is a function of the relative phase angles of the component beams. The greater the product of birefringence and optical path through the birefringent material, the greater the phase angle shift.
If the slow ray emerges with its phase angle 90.degree. behind the fast ray, the two beams totally interfere and the intensity of the beam falls to zero. If the slow ray emerges with its phase angle 180.degree. or some multiple of 180.degree. behind the fast ray, the two rays interefere constructively and there is no dimunition of beam intensity.
Assuming that the optic axis of a birefringent cell has been oriented 45.degree. from the parallel planes of polarization of polarizers on opposite sides thereof, the phase angle difference between the component beams is a function of the difference in refractive indices in the orthogonally propagating beam directions, the birefringence, .DELTA.n, the thickness, d, of the birefringent material, and the wavelength, .lambda., of light. Thus, the relative phase angle is: EQU .alpha.=2.pi.d.DELTA.n/.lambda.. (1)
The intensity of light passing through the second polarizer, neglecting any absorption losses, is given by the equation: EQU I=1-sin.sup.2 (.pi..DELTA.nd/.lambda.). (2)
The product .DELTA.nd is called the retardation. When the retardation equals M.lambda., where M is an integer, the intensity equals unity. When the retardation equals N.lambda./2, where N is an odd integer, the ordinary and extraordinary rays destructively interfere and the intensity falls to zero. If .DELTA.nd is kept constant while wavelength changes, intensity will vary in a cyclic manner. The value of M at the design wavelength .lambda. is called the order of the element.
According to Lyot, a filter is constructed by using a plurality of birefringent elements, the thicknesses of which increase in a geometrical progression whose ratio is two. The filter elements of Lyot were made of quartz and had their faces parallel to each other and normal to the light rays and their optical axes parallel to one another and forming 45.degree. angles with the planes of polarization of polarizers sandwiched between each cell. By passing a beam of light through such a stack of birefringent elements, each of which produces a different order of retardation, but subject to the restriction that the retardation of each element be integral multiples of a design wavelength, a narrow band pass filter can be constructed, suitable for use in high resolution applications.
The disadvantage of the filter described by Lyot is that it is very expensive and was designed for use at a single frequency, having very limited tunability. On the other hand, many applications require the use of tunable narrow bandwidth filters and attempts have been made to make widely tunable Lyot filters. Lyot, himself, suggested that it was possible to cause the center of the transmitted band to be movable by changing the temperature of the filter and this did indeed provide limited tunability.
If one changes the retardation by changing either or both birefringence, .DELTA.n, or thickness, d, the wavelength at which the fringe maxima occur will change. With most birefingent materials, such as quartz, calcite or mica, it is far easier to change thickness than to change birefringence. The Babinet-Soleil compensator is a commonly used birefringent element consisting of two quartz wedges. In sliding past each other, the effective thickness changes and with it the retardation. It is also possible to change the birefringence in some materials. This has been accomplished by utilizing stressed polymer films as variable retarders. A variable birefringence can also be induced in almost any liquid by applying a strong electric field (usually requiring thousands of volts). The Kerr cell is such a device. A variable birefringence can also be induced in certain ferroelectric crystals by applying a strong field.
All of these filters are either large, overly complex, or very expensive. The result has been that while quite a few versions of the Lyot filter have been developed over the years, they have all been very limited in application to situations where the high expense was acceptable. A relatively low cost Lyot filter, having useful levels of resolution, low stray-light ratios, and wide degrees of tunability has been unavailable heretofore.